One type of bandpass filter circuit used extensively in audio and other signal processing applications is the LC-resonant circuit. Such a circuit comprises resistive, inductive, and capacitive elements and is configured so that the gain of the circuit (i.e., the ratio of the input and output signal amplitudes V.sub.1 and V.sub.0 respectively) is a maximum at the resonant frequency .omega..sub.o (also called the peak frequency) where .omega..sub.o =1/.sqroot.LC. An exemplary frequency characteristic of such a circuit is shown in FIG. 1 where gain G is plotted against frequency .omega..
Another parameter of interest in such filters .omega..sub.o, is the quality factor Q, where Q equals the peak frequency divided by the peak's width (in terms of frequency) at -3dB of gain attenuation from the maximum. The Q is thus a measure of the sharpness of the peak. In a typical RLC resonant circuit, the Q may be varied by varying the value of the resistive element. For example, where a sharp peak is not desired, the peak may be broadened to give a flatter frequency response curve by adding what is called a Q-spoiling resistor. For a given resistance the Q of an RLC circuit depends on the ratio of the inductance and capacitance.
Many applications exist, especially in the audio field, for filters of the type described above which are tunable. Tunable filters are those which allow the peak frequency .omega..sub.o to be varied over a range of frequencies. Desirable properties of such tunable filters include independent control of peaking (Q) and tuned frequency (.omega..sub.o), control being proportional to the logarithm of the tuned frequency, a wide range over which the filter may be tuned, and the provision of a single control element each for peaking and frequency control. Heretofore, no conventional circuit has managed to provide all of these features in a satisfactory manner. For example, many tunable filter circuits provide a constant bandwidth as the peak frequency is changed rather than a constant Q. This means that the Q rises as the peak frequency is increased and vice-versa. The result, in an audio application, is like listening through a tube as only a narrow band of frequencies is accentuated which band becomes narrower as the peak frequency is raised. Other conventional filter circuits are able to maintain a nearly constant Q by the use of extra components to compensate for the basic properties of the circuit, but this approach will not work over a wide range of frequencies. In order to provide a truly constant Q while tuning over several octaves, conventional circuits have used two control elements mounted on a single shaft to control the peak frequency. This approach, however, is expensive and also can require good matching between the control elements which adds further to the cost. FIG. 2 shows an example of a conventional LRC filter circuit utilizing an op-amp A that allows control of peaking (i.e., Q) by varying resistance R and control of peak frequency by varying capacitance C and inductance L. If C and L change proportionately, the Q factor will remain constant as peak frequency is varied.